«TCHEBYCHEV'S INEQUALITY»に関連する英語の本
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1
Some Applications of Tchebychev's
Inequality to Analysis
Recombination of O and H atoms on the surfaces of catalysts, and the recombination of O atoms in the gas phase are discussed. (Author).
ROGER S. PINKHAM, RUTGERS
2
Principles of Uncertainty
(b) Find A and B such that AB = BA. 2.13 Tchebychev's Inequality and the (weak)
law of large numbers The weak law of large numbers (WLLN) is an important and
famous result in probability. It says that, under certain conditions, averages of ...
3
Probability and Random Variables
G P Beaumont. 10.3 AN APPLICATION OF TCHEBYCHEV'S INEQUALITY If X
has the binomial distribution with parameters n, p then we have seen that E(X) =
np, V(X) = npq. Applying Tchebychev's inequality "P4 Pr(lX—np|>k)< F for k>0.
4
The Theory of Probability and the Elements of Statistics
This proves Tchebychev's inequality. Tchebychev's Theorem : If £ t> €t> • • • » £•>
• • • ** <* sequence of pair- wise independent random variables possessing finite
variances which are uniformly bounded : Df, ^C, Df2^C Dfn < C then for any ...
Boris Vladimirovich Gnedenko, 2005
5
Surveying Natural Populations: Quantitative Tools for ...
(2.6) This relationship is known as Tchebychev's theorem or Tchebychev's
inequality. Let us assume that we wish to know what proportion of the samples is
within 2 standard deviations of the mean. In this case, our unit is a standard
deviation.
Lee-Ann C. Hayek, Martin A. Buzas, 2010
6
The Theory of Gambling and Statistical Logic
A notable application of Tchebychev's inequality lies in determining the point of
stochastic convergence—that is, the convergence of a sample probability to its
expected value. If, in Eq. 2-23, we replace the random variable X by the sample ...
(1°) (Tchebychev's inequality). // X((o) has finite variance V(X) , then we have P(\
X-E(X)\ >t)< V(X)/t2. (2°) (Kolmogorov's inequality). Assume that each random
variable Xn((o) has finite variance. Then, we have p(TM*n\Sk-E(Sk)\>t}<V(Sn)/t2
The ...
Takeyuki Hida, Masuyuki Hitsuda
8
Selected Papers on Differential Equations and Analysis
use of Tchebychev's inequality, a fixed-width confidence interval of given
confidence is naturally produced. Blum and Rosenblatt [BR69b] applied a similar
technique to obtain a fixed-width confidence interval of given confidence for the ...
9
Weighing the Odds: A Course in Probability and Statistics
Suppose that X\,X%, . . . is an infinite sequence of IID Random Variables, each in
£", each with mean p, and variance a~. Let Xi + X2 + • • • + Xn An . — n Then, for
every fixed e > 0, Proof. By Lemma 104E and Tchebychev's inequality, f2p(\A ,.
10
Discrete Multivariate Analysis: Theory and Practice
For example, Tchebychev's inequality asserts that if X is a random variable with
mean ,u and variance 02 < 00 and h is any positive number, then P{|X -— ,ul g ha
} 2 1 — h”. (14.4-4) We use Tchebychev's inequality to connect the 0,, o, notion of
...
Yvonne M. Bishop, Stephen E. Fienberg, Paul W. Holland, 2007
